{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Multiple Regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Shows how to calculate just the best fit, or - using \"statsmodels\" - all the\n",
    "corresponding statistical parameters.\n",
    "\n",
    "Also shows how to make 3d plots.\n",
    "\n",
    "Author: Thomas Haslwanter, Date:   April-2020"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    }
   ],
   "source": [
    "# The standard imports\n",
    "%pylab inline\n",
    "import pandas as pd\n",
    "# For the 3d plot\n",
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "from matplotlib import cm\n",
    "\n",
    "# For the statistic\n",
    "from statsmodels.formula.api import ols"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Generate and show the data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.colorbar.Colorbar at 0x2c1a54c0bc8>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(-5,5,101)\n",
    "(X,Y) = np.meshgrid(x,x)\n",
    "Z = -5 + 3*X-0.5*Y+np.random.randn(np.shape(X)[0], np.shape(X)[1])\n",
    "\n",
    "# Plot the figure\n",
    "fig = plt.figure()\n",
    "ax = fig.gca(projection='3d')\n",
    "surf = ax.plot_surface(X,Y,Z, cmap=cm.coolwarm)\n",
    "ax.view_init(20,-120)\n",
    "ax.set_xlabel('X')\n",
    "ax.set_ylabel('Y')\n",
    "ax.set_zlabel('Z')\n",
    "fig.colorbar(surf, shrink=0.6)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Simple plane fit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Best fit plane: [[-0.02345356 -0.02292034 -0.02272582 ...  0.01093157  0.01126141\n",
      "   0.01150601]\n",
      " [-0.00519251 -0.00503387 -0.00484759 ... -0.00465247 -0.00479241\n",
      "  -0.00504966]\n",
      " [-0.00519251 -0.00503387 -0.00484759 ... -0.00465247 -0.00479241\n",
      "  -0.00504966]\n",
      " ...\n",
      " [-0.1125771  -0.11001765 -0.10908396 ...  0.05247156  0.05405476\n",
      "   0.05522884]\n",
      " [-0.11492246 -0.11230968 -0.11135654 ...  0.05356472  0.0551809\n",
      "   0.05637944]\n",
      " [-0.11726782 -0.11460172 -0.11362912 ...  0.05465787  0.05630704\n",
      "   0.05753004]]\n"
     ]
    }
   ],
   "source": [
    "M = np.vstack((np.ones(len(X)), X, Y)).T\n",
    "bestfit = np.linalg.lstsq(M,Z, rcond=None)[0]\n",
    "print('Best fit plane:', bestfit)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Multilinear regression model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                      z   R-squared:                       0.988\n",
      "Model:                            OLS   Adj. R-squared:                  0.988\n",
      "Method:                 Least Squares   F-statistic:                 4.148e+05\n",
      "Date:                Tue, 14 Apr 2020   Prob (F-statistic):               0.00\n",
      "Time:                        22:12:14   Log-Likelihood:                -14304.\n",
      "No. Observations:               10201   AIC:                         2.861e+04\n",
      "Df Residuals:                   10198   BIC:                         2.864e+04\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept     -4.9912      0.010   -512.529      0.000      -5.010      -4.972\n",
      "x              3.0013      0.003    898.511      0.000       2.995       3.008\n",
      "y             -0.4981      0.003   -149.124      0.000      -0.505      -0.492\n",
      "==============================================================================\n",
      "Omnibus:                        0.633   Durbin-Watson:                   1.983\n",
      "Prob(Omnibus):                  0.729   Jarque-Bera (JB):                0.621\n",
      "Skew:                          -0.019   Prob(JB):                        0.733\n",
      "Kurtosis:                       3.006   Cond. No.                         2.92\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "# calculate fit, P-values, confidence intervals etc.\n",
    "X = X.flatten()\n",
    "Y = Y.flatten()\n",
    "Z = Z.flatten()\n",
    "# Convert the data into a Pandas DataFrame\n",
    "df = pd.DataFrame({'x':X, 'y':Y, 'z':Z})\n",
    "\n",
    "# Fit the model\n",
    "model = ols(\"z ~ x + y\", df).fit()\n",
    "\n",
    "# Print the summary\n",
    "print(model.summary())"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}
